Three Limit Order Book Models and Their Trade-Offs
Summary
The document outlines three approaches to modeling limit order books. Zero-intelligence models represent event frequencies and order sizes with relatively simple distributions. Two-dimensional flow models track changes to the best bid and ask queues. Queue-reactive models extend this approach by making event intensities depend on the current order-book shape.
The cited research is summarized as showing different strengths and limits: queue-reactive models capture liquidity dynamics well but tend to be too mean-reverting to reproduce larger-scale volatility, while zero-intelligence models show the opposite tendency. The middle approach is presented as theoretically interesting, though often less effective in practice. These are broad characterizations rather than a detailed comparative evaluation, and the document does not prescribe specific distributions or calibration procedures. It notes that the approaches can be extended to fragmented markets with multiple order books, at the cost of increasing model dimensionality.
Key ideas
- Zero-intelligence models represent order sizes and event frequencies with simple distributions.
- Two-dimensional flow models track events affecting the best bid and ask queues.
- Queue-reactive models condition event intensities on the current book shape.
- Queue-reactive models can capture liquidity dynamics but may understate macroscopic volatility.
- Modeling multiple exchanges is possible, though it increases the dimensionality.
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Full text
# Modeling orderbook shapes as distribution # Modeling orderbook shapes as distribution What are different distribution models typically used for generating orderbooks under high volatility, illiquidity, and multiple exchanges with different fees? ## Answer by lehalle (score 2) https://quant.stackexchange.com/a/77803 They are three levels of sophistication of order book models (there is a book on the topic: Abergel, Frédéric, Marouane Anane, Anirban Chakraborti, Aymen Jedidi, and Ioane Muni Toke. Limit order books Cambridge University Press, 2016) - Zero intelligence models - Farmer, J. Doyne, Paolo Patelli, and Ilija I. Zovko. "The predictive power of zero intelligence in financial markets" Proceedings of the National Academy of Sciences 102, no. 6 (2005): 2254-2259. - 2-dimension flows - Cont, Rama, and Adrien De Larrard. "Price dynamics in a Markovian limit order market" SIAM Journal on Financial Mathematics 4, no. 1 (2013): 1-25. - Queue Reactive models - Huang, Weibing, C-A L, and Mathieu Rosenbaum. "Simulating and analyzing order book data: The queue-reactive model" Journal of the American Statistical Association 110, no. 509 (2015): 107-122. In the first ones you focus on a few distributions (of order sizes, of frequency of events, etc) an univariate way and you replay them. In the second ones you focus on the trajectories of the two first queues (first bid and ask) and events that modify them. In the third ones you do the same but you condition the intensities of events by the shape of the orderbook. The take away of this line of research (spanned over more than 10 years) is that: the intensity of events conditioned by the shape of the order book reflects well the dynamics of liquidity (Queue Reactive), but not well the macroscopic volatility (it is toon mean reverting). This is the opposite for the Zero-intelligence approach. The middle approach is interesting from a theoretical viewpoint, but you can in general do better in practice. There is no reason to not use them in a fragmented setup (ie multiple order books), it is "just" that you will have to increase the dimension of the models.
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